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TRS Standard pair #516965252
details
property
value
status
complete
benchmark
enger-nonloop-while-lt.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n064.star.cs.uiowa.edu
space
EEG_IJCAR_12
run statistics
property
value
solver
NTI_22
configuration
default
runtime (wallclock)
0.308048963547 seconds
cpu usage
0.40473267
max memory
5.4370304E7
stage attributes
key
value
output-size
4178
starexec-result
NO
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- NO ** BEGIN proof argument ** The following pattern rule was generated by the strategy presented in Sect. 3 of [Emmes, Enger, Giesl, IJCAR'12]: [iteration = 3] while(true,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> while(true,s(s(_0)),s(s(_1))){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} We apply Theorem 8 of [Emmes, Enger, Giesl, IJCAR'12] on this rule with m = 1, b = 1, pi = epsilon, sigma' = {} and mu' = {}. Hence the term while(true,s(s(0)),s(s(_2))), obtained from instantiating n with 0 in the left-hand side of the rule, starts an infinite derivation w.r.t. the analyzed TRS. ** END proof argument ** ** BEGIN proof description ** ## Searching for a generalized rewrite rule (a rule whose right-hand side contains a variable that does not occur in the left-hand side)... No generalized rewrite rule found! ## Applying the DP framework... ## 2 initial DP problems to solve. ## First, we try to decompose these problems into smaller problems. ## Round 1 [2 DP problems]: ## DP problem: Dependency pairs = [while^#(true,_0,_1) -> while^#(lt(_0,_1),s(_0),s(_1))] TRS = {while(true,_0,_1) -> while(lt(_0,_1),s(_0),s(_1)), lt(s(_0),s(_1)) -> lt(_0,_1), lt(0,_0) -> true} ## Trying with homeomorphic embeddings... Failed! ## Trying with polynomial interpretations... This DP problem is too complex! Aborting! ## Trying with lexicographic path orders... Failed! ## Trying with Knuth-Bendix orders... Failed! Don't know whether this DP problem is finite. ## DP problem: Dependency pairs = [lt^#(s(_0),s(_1)) -> lt^#(_0,_1)] TRS = {while(true,_0,_1) -> while(lt(_0,_1),s(_0),s(_1)), lt(s(_0),s(_1)) -> lt(_0,_1), lt(0,_0) -> true} ## Trying with homeomorphic embeddings... Success! This DP problem is finite. ## A DP problem could not be proved finite. ## Now, we try to prove that this problem is infinite. ## Trying to prove non-looping nontermination # Iteration 0: non-looping nontermination not proved, 1 unfolded rule generated. # Iteration 1: non-looping nontermination not proved, 5 unfolded rules generated. # Iteration 2: non-looping nontermination not proved, 14 unfolded rules generated. # Iteration 3: success, non-looping nontermination proved, 34 unfolded rules generated. Here is the successful unfolding. Let IR be the TRS under analysis. IR contains the dependency pair while^#(true,_0,_1) -> while^#(lt(_0,_1),s(_0),s(_1)). We apply (I) of [Emmes, Enger, Giesl, IJCAR'12] to this dependency pair. ==> P0 = while^#(true,_0,_1){}^n{} -> while^#(lt(_0,_1),s(_0),s(_1)){}^n{} is in U_IR^0. We apply (VI) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the pattern rule lt(s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> lt(_2,_3){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} obtained from IR. ==> P1 = while^#(true,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} -> while^#(lt(_2,_3),s(s(_0)),s(s(_1))){_0->s(_0), _1->s(_1)}^n{_0->_2, _1->_3} is in U_IR^1. We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule lt(s(_0),s(_1)) -> lt(_0,_1) of IR. ==> P2 = while^#(true,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} -> while^#(lt(_2,_3),s(s(_0)),s(s(_1))){_0->s(_0), _1->s(_1)}^n{_0->s(_2), _1->s(_3)} is in U_IR^2. We apply (V) + (IX) of [Emmes, Enger, Giesl, IJCAR'12] to this pattern rule at position [0] using the rule lt(0,_0) -> true of IR. ==> P3 = while^#(true,s(_0),s(_1)){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} -> while^#(true,s(s(_0)),s(s(_1))){_0->s(_0), _1->s(_1)}^n{_0->s(0), _1->s(_2)} is in U_IR^3. This DP problem is infinite. Proof run on Linux version 3.10.0-1160.25.1.el7.x86_64 for amd64 using Java version 1.8.0_292 ** END proof description ** Total number of generated unfolded rules = 110
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